If the line `xcostheta+ysintheta=P` is the normal to the curve `(x+a)y=1,` then show `theta in (2npi+pi/2,(2n+1))uu(2npi+(3pi)/2,(2n+2)pi),n in Z`

If the line xcostheta+ysintheta=P is the normal to the curve (x+a)y=1, then show theta in (2npi+pi/2,(2n+1)pi)uu(2npi+(3pi)/2,(2n+2)pi),n in Z

The straight line xcostheta+ysintheta=2 will touch the circle x^2+y^2-2x=0 if (a) theta=npi,n in I Q (b) A=(2n+1)pi,n in I theta=2npi,n in I (d) none of these

The expression cos3theta+sin3theta+(2sin2theta-3)(sintheta-costheta) is positive for all theta in (2npi-(3pi)/4,2npi+pi/4),n in Z (2npi-pi/4,2npi+pi/6),n in Z (2npi-pi/3,2npi+pi/3),n in Z (2npi-pi/4,2npi+(3pi)/4),n in Z

If sin^3theta+sinthetacos^2theta=1,t h e ntheta is equal to (n in Z) (a) 2npi (b) 2npi+pi/2 (c) 2npi-pi/2 (d) npi

If cottheta-t a ntheta=s e ctheta , then theta is equal to 2npi+(3pi)/2, n Z b. npi+(-1)^npi/6,\ n Z c. npi+pi/2, n Z d. none of these

The value(s) of theta, which satisfy the equation : 2cos^3 3theta+4=3sin^2 3theta is/are (a) (2npi)/3+(2pi)/9,\ n in I (b) (2npi)/3-(2pi)/9,\ n in I\ (2npi)/5+(2pi)/5,\ n in I\ (d) (2npi)/5-(2pi)/5,\ n in I

If sintheta=1/2a n dcostheta=-(sqrt(3))/2, then the general value of theta is (n in Z)dot (a) 2npi+(5pi)/6 (b) 2npi+pi/6 (c)2npi+(7pi)/6 (d) 2npi+pi/4

The value(s) of theta , which satisfy 3-2\ costheta-4sintheta-cos2theta+sin2theta=0 is/are theta=2npi; n in I (b) 2npi+pi/2; n in I 2npi-pi/2; n in I (d) npi: n in I

If tan ptheta+cotqtheta=0 , then the genera value of theta is (A) ((2n-1)pi)/(2(p-q)) (B) (npi)/(p-q) (C) (npi)/(p+q) (D) ((2n+1)pi)/(2(p-q))

The sum of all the solutions of cottheta=sin2theta(theta!=npi, n integer) , 0lt=thetalt=pi, is (a) (3pi)/2 (b) pi (c) 3 pi/4 (d) 2pi